We did 3 tours with DC by Foot, including their night time monument bus tour. Their bus tour was great. Unfortunately the weather did not cooperate and it was pouring buckets of rain so hard that it was difficult for us to see a couple of the monuments from the bus. Before it started raining, we were able to get out at each monument and spend several minutes exploring it. Their tour guides are great, a real wealth of knowledge. Friendly, courteous, will whip out their smartphone to help find an answer to a question they may not know the answer to.
DC by Foot walking tours are free, you only tip your guide at the end whatever you think is an appropriate amount (we did $10/person). The bus tour will need to be reserved with a small fee (I believe $15/person last year, not sure on current prices) since there is a bus rental/bus driver involved that they have to pay. You then tip your tour guide the same at the end. We did go on another tour with another tour company while we were there and agreed that DC by Foot had better guides and provided an overall much better value.
We loved DC. Enjoy your first trip. It's a wonderful place with much to offer.
ETA: I might also recommend Stray Boots. Go to their website strayboots.com and their walking/text tours are so much fun! Your daughter might like the scavenger hunt aspect of it. We saw so many things we would have never otherwise seen, noticed or learned. They offer Groupons periodically, which will help cut the cost down.